CN110210690B - Optimal configuration method for micro synchronous phasor measurement unit of power distribution system - Google Patents

Abstract

The invention relates to an optimal configuration method for a micro synchronous phasor measurement unit of a power distribution system, which is technically characterized by comprising the following steps of: the method comprises the following steps: step 1, MSE is adopted as a standard state estimation precision evaluation index; step 2, based on the standard state estimation precision evaluation index in the step 1, starting from any consistent system real state, establishing a power distribution system mu PMU optimal configuration model by taking the MSE minimum as a target and the mu PMU configuration number as a constraint, and further seeking a mu PMU configuration scheme for enabling the state estimation MSE to be minimum; and 3, solving the optimal configuration model of the mu PMU of the power distribution system in the step 2 to obtain a final optimal configuration result of the mu PMU. The invention can adopt a commercial solver to quickly obtain a feasible solution with high quality, and provides a configuration scheme meeting engineering requirements for planning operators.

Description

Optimal configuration method for micro synchronous phasor measurement unit of power distribution system

Technical Field

The invention belongs to the technical field of electric power system quadratic programming, relates to an optimal configuration method for a micro synchronous phasor measurement unit of a power distribution system, and particularly relates to an optimal configuration method for a micro synchronous phasor measurement unit of a power distribution system.

Background

In recent years, many power failure accidents occurring at home and abroad highlight the weak points of insufficient elasticity and even extremely fragility of a power system to various natural disasters and disturbance events, and the construction of resilience power grids gradually becomes a national strategy for the intensive development of governments of various countries. The power distribution system directly faces to the user for power supply, and the power distribution system has insufficient elasticity and seriously threatens the reliable continuous power supply of the user.

The real-time situation awareness is an important premise for improving the elasticity of a power distribution system, and a power distribution network can be monitored in real time like a main network, so that the active awareness and intelligent decision of the running state of the power distribution network are realized. However, at the current level of distribution automation, real-time measurement is severely lacking and is not sufficient to accurately estimate the current operating state of the system. An Advanced Measurement Architecture (AMI) can periodically collect load data and power generation data of a user and can be used as pseudo Measurement to participate in state estimation. However, the strong dependence on the pseudo-metric often results in poor state estimation accuracy. Therefore, a certain amount of real-time measurement must be configured, and considering that the large scale of the power distribution system can only be installed with a small amount of measuring instruments under the condition of limited investment, but the problem that the measurement optimization configuration of the power distribution system is discrete, nonlinear and non-differentiable combination optimization is difficult to solve. The current micro synchronous phasor measurement units of the power distribution system are less researched, but the existing research mostly adopts a group intelligent algorithm to solve, so that the calculation efficiency is low, and a high-quality configuration scheme is difficult to obtain.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides the optimal configuration method of the micro synchronous phasor measurement unit of the power distribution system, which has the advantages of reasonable design, high calculation efficiency and capability of obtaining a high-quality configuration scheme.

The invention solves the practical problem by adopting the following technical scheme:

an optimal configuration method for a micro synchronous phasor measurement unit of a power distribution system comprises the following steps:

step 1, MSE is adopted as a standard state estimation precision evaluation index;

step 2, based on the standard state estimation precision evaluation index in the step 1, starting from any consistent system real state, establishing a power distribution system mu PMU optimal configuration model by taking the MSE minimum as a target and the mu PMU configuration number as a constraint, and further seeking a mu PMU configuration scheme for enabling the state estimation MSE to be minimum;

and 3, solving the optimal configuration model of the mu PMU of the power distribution system in the step 2 to obtain a final optimal configuration result of the mu PMU.

Moreover, the optimal design criteria of the MSE of step 1 are: let G ^-1 Trace of (c) is minimum, f _A :＝trace(G ^-1 ) And characterizing the state estimation mean square error.

Moreover, the optimal configuration model of the distribution system μ PMU in step 2 is as follows:

wherein:

G(x)＝H ^T R ^-1 (x)H (4)

R ^-1 (x)＝diag(w ₁ (x),…w _m (x)) (5)

wherein trace (-) is a matrix trace operation; h, R, G are respectively Jacobian matrix, measurement error covariance matrix and gain matrix of all configurable measurements at any system operating point, N _set For a set number of μ PMUs, w _ij,PF (x),w _ij,QF (x) The active and reactive measurement weight, w, of the beginning of the branch i-j _ij,PT (x),w _ij,QT (x) The active and reactive power measurement weights w for the i-j ends of the branch _i,PI (x),w _i,QI (x) For node i is injected withPower and reactive power measurement weight, w _i,V (x),w _i,A (x) Is the voltage amplitude and phase angle measurement weight of the node i, w _PMU ,w _AMI The weight of the two types of measurement of mu PMU and AMI,

respectively a network line set and a node set;

in matrix form, can be represented as:

wherein:

in the formula, H _i ,R _i ,G _i Respectively a Jacobian matrix, a measurement error covariance matrix and a gain matrix m measured in association with a node i at any system operating point _i And measuring quantity related to the node i, including injecting active and reactive power measurement into the node i, measuring voltage amplitude and phase angle of the node i, measuring active and reactive power at the initial end of the branch with the node i as the initial node, and measuring active and reactive power at the tail end of the branch with the node i as the final node.

Further, the specific steps of step 3 include:

(1) Performing load flow calculation to generate any operating point, and constructing G (x);

(2) Cholesky decomposition G (x) = L (x) L on matrix G (x) ^T (x)；

(3) To the upper triangular matrix L ^T (x) And the lower triangular matrix L (x) are respectively inverted through a back substitution process;

(4) The inverse of the matrix G (x) is G ^-1 (x)＝[L ^T (x)] ^-1 [L(x)] ^-1 ；

(5) Sending the model into an integer programming solver, and setting N _set ＝1～n _b Sequentially solving for n _b A model, obtaining a target value with N _set Increase and decreaseAnd selecting a turning point of the curve, wherein the turning point is quickly reduced to be gentle, as a final mu PMU optimal configuration result.

The invention has the advantages and beneficial effects that:

1. the invention provides a high-precision state-sensing-oriented optimal configuration method for a mu PMU (phasor measurement unit) of a power distribution system, which comprises the steps of firstly, on the basis that AMI (amplitude measurement indicator) measurement meets network observability, taking state estimation mean square error minimum as a target, substituting any consistent system running state as a parameter into a state estimation error covariance matrix, and establishing a mu PMU optimal configuration model; secondly, performing Cholesky decomposition on the gain matrix, and explicitly expressing the objective function by adopting a decision variable, so that a high-quality feasible solution can be quickly obtained by adopting a commercial solver; finally, simulation tests were performed using the IEEE 33 node and 69 node power distribution systems.

2. The model of the invention takes AMI measurement to meet network observability as the premise, takes minimum state estimation mean square error as the target, and takes any consistent system running state as a parameter to substitute into a state estimation error covariance matrix;

3. according to the method, cholesky decomposition is carried out on the gain matrix, and the objective function is explicitly expressed by adopting the decision variable, so that a high-quality feasible solution can be quickly obtained by adopting a commercial solver, and a configuration scheme meeting engineering requirements is provided for planning operators;

4. according to the method, a mu PMU optimal configuration model is established by taking high-precision state sensing as a target, a decision variable is explicitly expressed by a target function through Cholesky decomposition on a gain matrix, the solving speed and the resolving quality are greatly improved, and compared with the existing method, the method can obtain a feasible scheme with higher quality in a shorter time.

Drawings

FIG. 1 is a wiring diagram of a 33 node power distribution system of the present invention;

FIG. 2 is a graph of two method MSE curves for a 33-node system of the present invention;

fig. 3 is a comparison graph of state estimation accuracy for two optimal PMU configurations of the present invention versus prior methods.

Detailed Description

The embodiments of the invention will be described in further detail below with reference to the accompanying drawings:

an optimal configuration method for a miniature synchronous phasor measurement unit of a power distribution system comprises the following steps:

step 1, MSE is adopted as a standard state estimation precision evaluation index;

the optimal design criteria for the MSE are: let G ^-1 Trace of (c) is minimum, f _A :＝trace(G ^-1 ) Characterizing the state estimation mean square error;

the state estimation objective function can only describe the fitting condition of the estimated value to the measured value, and the state estimation objective function cannot be used for evaluating the state estimation precision due to the influence of measurement noise. The gain Matrix G is also called Fisher Information Matrix (FIM), and includes system Information obtained by measurement, and its inverse Matrix G ^-1 The covariance matrix of the state estimation error represents the estimation effect of the measurement system, and is an important index for evaluating the configuration quality of the measurement system. General choice of G in the estimation field ^-1 The certain scalar function f as the state estimation accuracy evaluation index is a quantitative evaluation index for different angles of the state estimation confidence ellipsoid, for example:

1) E-optimal design criteria: let G ^-1 Maximum eigenvalue of (c) is minimum, f _E :＝λ _max (G ^-1 ) Characterizing the worst error variance;

2) A-optimal design criteria: let G ^-1 Trace of (c) is minimum, f _A :＝trace(G ^-1 ) Characterizing the state estimation Mean Square Error (MSE);

3) M-optimal design criteria: let G ^-1 Maximum diagonal element of (c) minimum, f _M :＝max{[G ^-1 ] _ii }, characterizing the maximum state estimation error variance;

4) D-optimal design criteria: let f _D :＝log detG ^-1 Characterizing the volume of a confidence ellipsoid, minimizing f _D Equivalent to maximizing log detG.

The method adopts MSE as a state estimation precision evaluation index to establish a mu PMU optimal configuration model, namely an A-optimal design standard.

Step 2, based on the standard state estimation precision evaluation index in the step 1, starting from any consistent system real state, establishing a power distribution system mu PMU optimal configuration model by taking the MSE minimum as a target and the mu PMU configuration number as a constraint, and further seeking a mu PMU configuration scheme for enabling the state estimation MSE to be minimum;

the real operation state of the system at a certain moment depends on the load size of all load nodes of the system, and at the moment, all possible mu PMU configuration schemes can obtain unbiased estimation of the real state of the system through WLS estimation.

Suppose at some time t the true state of the system is x _t Consider mu PMU configuration scheme C ₁ And C ₂ The estimated states are x respectively ₁ And x ₂ Suppose scheme C ₁ Estimation accuracy better than scheme C ₂ . If a random measurement error is set on the basis of the real running state at the moment, and N times of state estimation calculation are executed, the state estimation errors of all mu PMU configuration schemes are expected to be the same, are equal to the real running state at the moment and are influenced by the random error, and the voltage estimation MSE of each node of different mu PMU configuration schemes is different from each other. Namely:

at different moments, the real state of the system is in a slowly changing quasi-steady state, but the precision comparison of different mu PMU configuration schemes is not changed, namely, at other moments, the scheme C ₁ The state estimation accuracy of (2) is still higher than C ₂ 。

Based on the above analysis, the present invention seeks a μ PMU configuration scheme that minimizes the state estimation MSE, starting from any consistent system true state.

The specific steps of establishing the optimal configuration model of the mu PMU of the power distribution system in the step 2 comprise:

(1) For having n _b A node, n _l Distribution network of strip branches, configurable n _b Measurement of individual voltage amplitudes, n _b An electricityPhase angle measurement, n _b Individual injected active power measurement, n _b Individual injection reactive power measurement, n _l Active power measurement at the beginning of each branch, n _l Reactive power measurement at starting end of each branch, n _l Active measurement of the end of each branch, n _l Reactive power measurement of each branch end, totaling 4 (n) _b +n _l ) Measuring in real time; if a mu PMU is configured at a certain node, the active and reactive measurements of the tail end of an upstream branch of the node, the active and reactive measurements of the initial ends of all downstream branches, the active and reactive measurements injected by the node, and the amplitude and phase angle measurements of the voltage of the node can be obtained; otherwise, the node only has the injected active and reactive measurement provided by AMI. When there is at least one phase angle measurement in the system, the reference node may not be set;

(2) For each node whether μ PMU is configured or not, a 0-1 variable is introduced:

(3) With the MSE minimum as a target and the configuration quantity of the mu PMU as a constraint, establishing the following mu PMU optimal configuration model:

wherein:

G(x)＝H ^T R ^-1 (x)H (4)

R ^-1 (x)＝diag(w ₁ (x),…w _m (x)) (5)

wherein trace (-) is matrix trace operation, H, R, G are respectively Jacobian matrix, measurement error covariance matrix and gain matrix of all configurable measurements at any system operating point, N _set For a set number of μ PMUs, w _ij,PF (x),w _ij,QF (x) The active and reactive measurement weight, w, of the beginning of the branch i-j _ij,PT (x),w _ij,QT (x) The active and reactive power measurement weights w for the i-j ends of the branch _i,PI (x),w _i,QI (x) Injecting active and reactive measurement weights, w, for node i _i,V (x),w _i,A (x) Is the voltage amplitude and phase angle measurement weight of the node i, w _PMU ,w _AMI The weight of the two types of measurement of mu PMU and AMI,

respectively a network line set and a node set.

In matrix form, can be represented as:

wherein:

in the formula, H _i ,R _i ,G _i Respectively a Jacobian matrix, a measurement error covariance matrix and a gain matrix m measured in association with a node i at any system operating point _i And measuring quantity related to the node i, including active and reactive power measurement injected into the node i, voltage amplitude and phase angle measurement of the node i, active and reactive power measurement of the initial end of the branch with the node i as the initial node and active and reactive power measurement of the tail end of the branch with the node i as the final node.

As can be seen, the model weights all measurementsMultiplying the measured weight by the mu PMU decision variable to obtain a new measurement weight; when the decision variable of a PMU is 0, all measured weights become 0. Wherein, for the measurement of injected active and reactive power, if the node is configured with mu PMU, its weight is w _PMU Otherwise, its weight is w _AMI . Even if all nodes are not configured with mu PMUs, the network can still be kept observable because AMI can still provide node injection measurements with non-zero weights.

Step 3, solving the optimal configuration model of the power distribution system mu PMU in the step 2;

the model objective function involves a non-linear matrix inversion operation. When the network is observable, G (x) is a symmetric positive definite matrix, and an algebraic expression of an inverse matrix can be obtained by adopting Cholesky decomposition. The Cholesky decomposition of the symmetric positive definite matrix is as follows:

the diagonal elements of the lower triangular matrix L (x) are calculated as:

the off-diagonal element calculation formula is:

in the order i =1,2 … n _b By alternately executing the equations (12) and (13), all elements of the matrix L (x) can be represented by the decision variable x.

The specific steps of the step 3 comprise:

further, the specific steps of step 3 include:

(1) Performing load flow calculation to generate any operating point, and constructing G (x);

(2) Cholesky decomposition G (x) = L (x) L on matrix G (x) ^T (x)；

(3) To the upper triangular matrix L ^T (x) And the lower triangular matrix L (x) are respectively inverted through a back substitution process;

(4) The inverse of the matrix G (x) is G ^-1 (x)＝[L ^T (x)] ^-1 [L(x)] ^-1 ；

(5) Sending the model into an integer programming solver, and setting N _set ＝1～n _b Sequentially solving for n _b A model, obtaining a target value with N _set Increasing and decreasing curves, and selecting the turning point where the curve rapidly decreases to be smooth as the final mu PMU optimal configuration result.

In the present embodiment, the proposed method is tested by taking IEEE 33 node power distribution system as an example. The wiring diagram is shown in fig. 1. C + + programming is adopted, nonlinear programming software LocalSolver 8.5 is called to solve the model, and by designing a matrix template class and instantiating the matrix template class by adopting a LocalSolver expression, cholesky decomposition of the gain matrix is realized. LocalSolver is a heuristic optimization engine based on a local search technology, is focused on solving large-scale combinatorial optimization and mixed integer nonlinear problems, and has shown excellent solving performance in various fields. All tests were performed on a personal laptop computer equipped with an i5-7200U processor and 8G memory.

Adopting per unit value calculation, selecting any power flow solution as a parameter to substitute into a state estimation covariance matrix construction model, and setting the AMI measurement weight and the PMU measurement weight as 1/0.1 respectively ² 、1/0.0005 ² . Let N _set =1 to 33, the model is solved by the method mentioned, and each N is calculated _set The following optimal configuration scheme. By means of trial, for a 33-node system, the target function is not changed any more when the calculation time of the solver reaches 1min, and therefore the calculation time of the solver is set to 1min each time; meanwhile, MATLAB built-in Genetic Algorithm (GA) is adopted for comparison, algorithm parameters adopt default values, and the best result is calculated for ten times. The two methods adopt different system operating points to construct a model, wherein MSE is along with N _set The variation curve is shown in fig. 2, where M1 is the proposed method. As can be seen, both methods estimate MSE with N _set The increase rapidly decreases; when more than 3 mu PMUs are configured, the improvement of the state estimation precision is slowed down by continuously increasing the mu PMUs. Therefore, high-precision state sensing can be realized by only configuring a small amount of mu PMUs.

To verify the results, 100 state estimation calculations were performedAnd comparing the state estimation precision under the optimal mu PMU configuration scheme by using the two methods. The measurement truth value is obtained by load flow calculation, all node loads are set to randomly fluctuate within the range of 0.8-1.2 times of rated load values, and all mu PMU measurement and load pseudo measurement are respectively set with 0.05% and 10% Gaussian random errors. N is a radical of _set Two methods MSE curves when =2 to 5 are shown in fig. 3. As can be seen from the figure, the optimal mu PMU configuration scheme MSE obtained by the method is smaller than the GA solution result, the state estimation precision is higher, and the effectiveness of the method is verified. N is a radical of hydrogen _set From 2 to 5, the MSE of the two schemes is more and more different, because the quality of the solution of the GA method depends on the size of the search space, and as the search space increases, larger clusters and more time are required to obtain a feasible solution of high quality. Combining the trade-off between investment and state estimation accuracy, the planner can configure the PMU at 3 nodes 15, 19, 28.

It should be emphasized that the examples described herein are illustrative and not restrictive, and thus the present invention includes, but is not limited to, those examples described in this detailed description, as well as other embodiments that can be derived from the teachings of the present invention by those skilled in the art and that are within the scope of the present invention.

Claims (1)

1. A method for optimizing and configuring a micro synchronous phasor measurement unit of a power distribution system is characterized by comprising the following steps: the method comprises the following steps:

step 1, MSE is adopted as a standard state estimation precision evaluation index;

step 2, based on the standard state estimation precision evaluation index in the step 1, starting from any consistent system real state, establishing a power distribution system mu PMU optimal configuration model by taking the MSE minimum as a target and the mu PMU configuration number as a constraint, and further seeking a mu PMU configuration scheme for enabling the state estimation MSE to be minimum;

step 3, solving the optimal configuration model of the mu PMU of the power distribution system in the step 2 to obtain a final optimal configuration result of the mu PMU;

the optimal design criteria of the MSE of the step 1 are as follows: let G ^-1 Trace of (c) is minimum, f _A :＝trace(G ^-1 ) Characterizing the state estimation mean square error;

the optimal configuration model of the power distribution system mu PMU in the step 2 is as follows:

wherein:

G(x)＝H ^T R ^-1 (x)H

R ^-1 (x)＝diag(w ₁ (x),…w _m (x))

w _ij,PF (x)＝w _PMU x _i

w _ij,QF (x)＝w _PMU x _i ,i-j∈L

w _ji,PT (x)＝w _PMU x _i

w _ji,QT (x)＝w _PMU x _i ,j-i∈L

w _i,PI (x)＝w _PMU x _i +w _AMI (1-x _i )

w _i,QI (x)＝w _PMU x _i +w _AMI (1-x _i ),i∈B

w _i,V (x)＝w _PMU x _i

w _i,A (x)＝w _PMU x _i ,i∈B

wherein trace (-) is a matrix trace operation; h, R, G are respectively Jacobian matrix, measurement error covariance matrix and gain matrix of all configurable measurements at any system operating point, N _set For a set number of μ PMUs, w _ij,PF (x),w _ij,QF (x) The active and reactive measurement weight, w, of the beginning of the branch i-j _ji,PT (x),w _ji,QT (x) For the active and reactive measurement weights, w, at the j-i ends of the branches _i,PI (x),w _i,QI (x) Injecting active and reactive measurement weights, w, for node i _i,V (x),w _i,A (x) The amplitude and phase angle of the voltage at node i are measured as weight, w _PMU ,w _AMI The weight of the two types of measurement of mu PMU and AMI,

respectively a network line set and a node set;

in matrix form, can be represented as:

wherein:

in the formula, H _i ,R _i ,G _i Respectively a Jacobian matrix, a measurement error covariance matrix and a gain matrix m of the node i correlation measurement at any system operating point _i Measuring quantity related to the node i, including injecting active and reactive power measurement into the node i, measuring voltage amplitude and phase angle of the node i, measuring active and reactive power at the initial end of a branch taking the node i as an initial node and measuring active and reactive power at the tail end of the branch taking the node i as a final node;

the specific steps of the step 3 comprise:

(1) Performing load flow calculation to generate any operating point, and constructing G (x);

(2) Cholesky decomposition G (x) = L (x) L on matrix G (x) ^T (x)；

(3) To the upper triangular matrix L ^T (x) And the lower triangular matrix L (x) are respectively inverted through a back substitution process;

(4) The inverse of the matrix G (x) is G ^-1 (x)＝[L ^T (x)] ^-1 [L(x)] ^-1 ；

(5) Sending the model into an integer programming solver, and setting N _set ＝1～n _b Sequentially solving for n _b A model, obtaining a target value with N _set Increasing and decreasing curves, and selecting the turning point where the curve rapidly decreases to be smooth as the final mu PMU optimal configuration result.

Images